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Outline
The Geometry of Music
Musical Harmony from First Principles
Pythagorean, Just, and Equal Tempered Scales
Euclidean Rhythms, Even Distribution, and Bjorklund's Algorithm
Keyboards in Geogebra
The Geometry of Music
Author:
Steve Bleiler
Topic:
Geometry
An exploration of musical scales, temperament, and algorithmic keyboard design.
Table of Contents
Musical Harmony from First Principles
The Basic Sine Wave
Build a Sound Wave
Dyadic Harmony in the Plane
Visualize Two Note Harmonies with Lissajous Diagrams
Visualize 3 Note Chords with Lissajous Diagrams in 3-D
The Chordal Spirograph
Hearing Just Intervals
Hearing 3 Note Just Chords
Pythagorean, Just, and Equal Tempered Scales
Just Scale
Pythagorean Scale
Equal Tempered Scales
Contrasting Chords in Different Temperaments
Circle of Chords in n-ET
Extended Chords
Euclidean Rhythms, Even Distribution, and Bjorklund's Algorithm
A Drum Machine for Euclidean Rhythms
Even Distribution and Euclidean Rhythms
Generating All Euclidean Rhythms
Keyboards in Geogebra
Generalized Equal Tempered Keyboard
Euclidean Equal Tempered Keyboard
An Hexagonal Just Lattice Keyboard
An Hexagonal Just Lattice Keyboard
A Playable 5-Limit Tonality Diamond
A Playable n-limit Tonality Diamond
The Virtual Tonal Plexus
Next
The Basic Sine Wave
New Resources
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Quadratic Equations
Hypergeometric Distribution
